Worksheet - Institute for Advanced Study
Worksheet
Rhombic Dodecahedron – Hidden Within or
Surrounding the Cube?
Name_________________________________
Consider a cube with one face ADBC.
[pic]
1. How many faces does the cube have? __________ edges?________ vertices?__________
2. Each face has ________________diagonals. Total face diagonals per cube? ______________________
3. Diagonal ([pic]) and adjacent edges ([pic]) form what type of geometric figure? _____________ Are all such figures of the cube congruent? ____________ Why? ________________________________________________________
4. Assuming an edge length of 2 units, calculate the length of each face diagonal._____________________
5. When 6 congruent square pyramids are put together with their apexes inward they form a cube as shown below. The non-base edges of the pyramids form the interior diagonals of the cube and are ______________ as long as a lateral edge of each pyramid.
[pic] [pic]
Square Pyramid Cube Formed by Square Pyramids
6. Look at the above diagram of the square pyramid and use the Pythagorean Theorem to find each length.
|Length of edge of base |2 units |
|Length of altitude of pyramid | |
|Length of altitude of lateral face | |
|Length of lateral edge of pyramid | |
7. When the cube is surrounded by a jacket of 6 square pyramids, a new polyhedron is created. How many faces does it appear to have? ______________What are the measures of the dihedral angles formed where three faces meet at a vertex on the new polyhedron? _________________________
8. Show/explain with words or diagrams why the triangles of two adjacent pyramids create a flat rhombic face of the new polyhedron.
9. Use the diagrams below to help calculate the lengths of the long and short diagonals. You may also find the Zome( tool model/straw model helpful.
[pic] [pic]
[pic]
|Length of edge | |
|Length of short diagonal | |
|Length of long diagonal | |
9. The rhombic dodecahedron packs space. Put together several of the rhombic dodecahedrons to see this amazing property. Explain in words and/or diagrams why you think this works.
11. Show your calculations for each of the following.
a. Find the volume of the cube. ________________________
b. Find the volume of the square based pyramid using at least two techniques.
__________________________
c. Find the volume of the rhombic dodecahedron.
______________________________________________
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- finding missing angles worksheet
- indefinite integrals calculus
- z score practice worksheet
- 6th grade reading writing argumentative texts unit
- relapse prevention plan worksheet
- worksheet on bias in the media weebly
- worksheet institute for advanced study
- math lesson plan
- domain and range worksheet arizona state university
- biodiversity worksheet
Related searches
- institute for vaccine safety hopkins
- kavli institute for theoretical science
- institute for mathematical sciences
- unesco institute for statistics database
- the institute for effective education
- allure institute for plastic surgery
- andrews institute for orthopaedics sports
- unesco institute for statistics uis
- institute for plastic surgery
- institute for quality education indiana
- unesco institute for statistics 2018
- american physician institute for advanced